Multifractal Analysis in Characterizing Adsorption Pore Heterogeneity of Middle- and High-Rank Coal Reservoirs

[Image: see text] Nanopore heterogeneity has a significant effect on adsorption, desorption, and diffusion processes of coalbed methane. The adsorption pore size distribution heterogeneity was calculated by combining N(2) with CO(2) adsorption data, and factors affecting multifractal and single-fractal dimensions were studied. The results indicate that pore size distribution of micropores (with pore diameters smaller than 2 nm) and meso–macro-pores (with pore diameters between 2 and 100 nm) in coal samples exhibit typical multifractal behavior. The overall heterogeneity of micropores in high-rank coal samples is higher than that in the middle-rank coal samples. The low-probability measure areas control the overall heterogeneity of pores with diameters of 0.40–1.50 nm. The high-probability measure area heterogeneity and spectral width ratio have a higher linear correlation with coal rank and pore structure parameters than those of low-probability measure areas. Heterogeneity of high-probability measure areas and overall pore size distribution are controlled by pores with diameters of 0.72–0.94 nm. Multifractal parameters of meso–macro-pores have no clear relationship with coal rank. The pore volume of 2–10 nm diameter shows a good linear correlation with heterogeneity of low-probability measure areas, and pores of this diameter range are the key interval that affected pore size distribution heterogeneity. The single-fractal dimension obtained using the Frenkel–Halsey–Hill (FHH) model shows a positive linear correlation with heterogeneity of the low-probability measure areas. It indicates that this parameter can effectively characterize the pore size distribution heterogeneity of low-probability measure areas in meso–macro-pores.